Deflation-based Identification of Nonlinear Excitations of the 3D Gross--Pitaevskii equation

Understand

We present previously unknown solutions to the 3D Gross--Pitaevskii equation describing atomic Bose-Einstein condensates.

• This model supports elaborate patterns, including excited states bearing vorticity.
• The discovered coherent structures exhibit striking topological features, involving combinations of vortex rings and multiple, possibly bent vortex lines.
• Although unstable, many of them persist for long times in dynamical simulations.